5 Orthocenter Things That Geometry Kids Should Know
The Orthocenter cuts each altitude into two parts whose products for each altitude are equal.
AH x HF = CH x HD = BH x HE
Distance from Orthocenter to Vertex, Length of Opposite Side, Circumcircle Diameter
AH2 + BC2 = BH2 + AC2 = CH2 + AB2 = Diameter2
Distances from the Orthocenter to the Vertices.
AH + BH + CH = Incircle Diameter + Circumcircle Diameter
Distances from the Orthocenter to the Vertices 2
Distance from Orthocenter to Vertex = 2 x Distance from Circumcenter to opposite side
Orthocentric Quartet
Given 3 points and their Orthocenter, any of the 4 points is the Orthocenter of the other 3 points.